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We present a general "fit-free" method for measuring the equation of state(EoS) of a scale-invariant gas. This method, which is inspired from theprocedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitarythree-dimensional Fermi gas, provides a general formalism which can be readilyapplied to any quantum gas in a known trapping potential, in the frame of thelocal density approximation. We implement this method on a weakly-interactingtwo-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thoulesstransition, and determine its EoS with unprecedented accuracy in the criticalregion. Our measurements provide an important experimental benchmark forclassical field approaches which are believed to accurately describe quantumsystems in the weakly interacting but non-perturbative regime.

Fit-free determination of scale invariant equations of state: application to the 2D Bose gas across the Berezinksii-Kosterlitz-Thouless transition